Uve is from Estonia and holds a bachelor's degree in adult education from Tallinn University. During his undergraduate studies, Uve was an avid intervarsity debater and continues to support and promote debate as an engaging method for civic education.

After graduating from Tallinn University in 2009, he spent five years managing the Unitas Foundation, an educational non-profit based in Tallinn. Uve helped launch a range of initiatives for researching and teaching history in contemporary ways, from setting up digital archives to developing web-based and participative educational methods. These projects include co-operation with the Stanford University Libraries.

Working with reconciliatory history and human rights education programs, his expertise covers the intersection of national identities, history and politics, especially in the context of Estonia and the Baltic states. He has also written on these themes for Estonian and international periodicals.

Uve is currently researching a similar range of topics pertinent to Ukraine in the aftermath of the 2014 revolution.